A note on the random greedy triangle-packing algorithm

Details A note on the random greedy triangle-packing algorithm A note on the random greedy triangle-packing algorithm

2010-04-14

arxiv.org/abs/1004.2418v1

Mathematics

Combinatorics

10 pages

Scientific paper

The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. We begin with a complete graph on $n$ vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is chosen uniformly at random from the collection of all remaining triangles. This stochastic process terminates once it arrives at a triangle-free graph. In this note we show that with high probability the number of edges in the final graph is at most $ O\big( n^{7/4}\log^{5/4}n \big) $.

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